Like if I am an average Spanish or European citizen and I hear stories about the conquistadores and their adventures in South America would I react with disgust at the way they treated the natives or would I think the natives were just a group of godless savages who got what was coming to them ?
What about the elites and nobles, how did they feel about the conquistadores ?
Quick and easy answer: yes. longer answer: The Church generally viewed Natives as people who needed to be saved, so they were not happy about the cruelty towards the Indigenous peoples by the Conquistadores (though they still took some of the stolen Gold). The Church wanted missionaries to spread the word and convert the Natives. Other countries viewed the Spanish in very negative terms even before the conquistadores actions... so they tended to jump on the bandwagon quite strongly to fuel anti-Spanish sentiments. This benefited them a bit too since it allowed them to portray themselves as the "good colonist" in contrast in their colonization attempts in the 16th century, and their successful endeavors in the 17th and 18th. These anti-Spanish sentiments were strongest in Protestant regions that had warred with Spain in the 16th century, such as England, The Netherlands, and various German states.
TL;DR: People did feel bad for the Natives to a degree, but mostly, they just didn't like the Spanish and jumped on the anti-Spanish bandwagon, using the plight of the Natives as one of their arguments.